CN113761729A - Wood transverse grain pressure-bearing constitutive relation model construction method and device based on wood weak phase structure and storage medium - Google Patents

Wood transverse grain pressure-bearing constitutive relation model construction method and device based on wood weak phase structure and storage medium Download PDF

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CN113761729A
CN113761729A CN202110978550.0A CN202110978550A CN113761729A CN 113761729 A CN113761729 A CN 113761729A CN 202110978550 A CN202110978550 A CN 202110978550A CN 113761729 A CN113761729 A CN 113761729A
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CN113761729B (en
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武国芳
钟永
傅峰
任海青
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Research Institute of Wood Industry of Chinese Academy of Forestry
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Research Institute of Wood Industry of Chinese Academy of Forestry
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Abstract

The utility model provides a timber striation pressure-bearing constitutive relation model construction method, device and storage medium based on timber weak phase structure, including: constructing a stress-strain relation of the wood in an elastic stage according to Hooke's law of transversely viewing isotropic materials; according to the stress characteristic of wood cross grain bearing, separating equivalent stress causing volume deformation of wood from offset stress causing shear deformation of the wood in a wood cross grain plane, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress; constructing a plastic flow equation in the wood transverse grain plane according to the non-correlation flow rule; constructing a hardening equation in the plane of the wood cross grain according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression of the wood and the yield stress during the bidirectional compression of the wood; and constructing the stress-strain relation in the wood grain-following plane. The method can better simulate the compression deformation of the volume of the wood transverse striation when being pressed.

Description

Wood transverse grain pressure-bearing constitutive relation model construction method and device based on wood weak phase structure and storage medium
Technical Field
The disclosure belongs to the technical field of wood science and engineering structure simulation, and particularly relates to a wood cross grain pressure-bearing constitutive relation model construction method and device based on a wood weak phase structure, and a storage medium.
Background
The wood is a biomass material, the complex mechanical properties of the wood are represented by brittle failure under the action of tensile force or shearing force, plastic deformation under the action of pressure, unequal tensile and compressive strengths, and the wood also has the characteristics of creep deformation, mechanical adsorption, fracture, load duration effect and the like.
The constitutive relation model of wood is a mathematical expression for describing the relation of wood stress, strain, time and the like, and generally comprises stress-strain relation of an elastic stage, strength criterion, hardening, softening, plasticity development rule and the like. In the aspect of building a wood constitutive relation model, at present, a lot of researches are carried out on strength criteria, the strength criteria used for wood in the existing researches comprise a maximum principal stress criterion, a Tsai-Wu criterion, a Hankinson formula, a Hoffman criterion, a Norris criterion, a Yamada-Sun criterion, a Hashin criterion and the like, but the researches on the subsequent plastic development, softening and hardening and the like are not carried out. When the wood transverse striation is pressed, the load-displacement curve presents 3 different stages: firstly, a linear elastic section, then the wood enters a platform stage, namely, the load is almost unchanged, but the deformation is continuously developed, and finally, a strengthening stage, namely, the deformation is slightly increased, and the load is rapidly increased.
When the wood cross grain bears pressure, particularly when the wood cross grain is locally pressed, the error of the deformation and the actual measurement result predicted by the finite element model is large. One very important reason for this phenomenon is that most constitutive relation models are developed based on metal constitutive models, the plastic deformation of metal materials is not compressible, and the strength criterion is not influenced by hydrostatic stress. The wood is a porous material and has obvious volume compression deformation under the compression load, namely the porous structure of the wood is characterized by a weak phase structure when wood cross grains bear pressure, and the load displacement curve characteristic of the wood under the cross grain compression load is closely related to the change of an internal gap.
Disclosure of Invention
The present disclosure is directed to solving at least one of the technical problems of the prior art.
Therefore, the method for constructing the wood cross grain pressure-bearing constitutive relation model, which can consider the phenomena of large deformation and secondary hardening during wood compression and better simulate the volume compression deformation of wood cross grains during pressure, and thus overcomes the defect that the existing method seriously underestimates the compression deformation of the wood cross grains, comprises the following steps:
separating the stress and strain of the wood along the grain direction and the transverse grain direction;
constructing a stress-strain relation of the wood in an elastic stage according to Hooke's law of transversely viewing isotropic materials;
according to the stress characteristic of wood cross grain bearing, separating equivalent stress causing volume deformation of wood from offset stress causing shear deformation of the wood in a wood cross grain plane, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
constructing a plastic flow equation in the wood transverse grain plane according to the non-correlation flow rule;
constructing a hardening equation in the plane of the wood cross grain according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression of the wood and the yield stress during the bidirectional compression of the wood;
and (3) constructing a stress-strain relation in the wood grain-following plane by adopting a linear elastic model or a strength criterion independent of the wood grain-crossing plane.
The method for constructing the wood cross grain pressure-bearing constitutive relation model provided by the embodiment of the first aspect of the disclosure has the following characteristics and beneficial effects:
the method is used for establishing a constitutive relation model of the wood based on a typical weak phase structure of the porous characteristic of the wood, and can simulate the characteristics of three typical stages of linear elasticity-platform stage-strengthening in compression, wherein the tensile strength of the wood transverse striation is unchanged. And because the pore compression is considered, the equivalent stress causing the volume deformation of the wood in the wood cross grain plane is separated, the relation between the yield stress and the strain of the wood in the unidirectional compression is used as input, the relation between the yield stress and the plastic strain in the bidirectional compression is obtained through conversion, and the change of a yield equation is controlled by tracking the change of the volume strain of the wood, so that the volume compression and the large deformation existing in the pressure bearing of the wood cross grain are simulated, and the matching degree of the compression deformation of the cross grain obtained through simulation and a test measured value is high. The problem of the current model underestimate striation compression deformation is solved. In addition, the yield surface equation, the flow equation and the hardening equation of the wood cross grain bearing are established, each parameter in the established model has physical significance, operations such as data fitting and the like are not needed, and the parameter acquisition is simple and convenient.
In some embodiments, the yield surface equation for the elasto-plastic phase in the wood grain plane is constructed as f (p, q), expressed as:
Figure BDA0003228264340000021
Figure BDA0003228264340000022
Figure BDA0003228264340000023
Figure BDA0003228264340000024
Figure BDA0003228264340000025
wherein p is equivalent stress in the wood transverse grain plane and mainly causes volume compression or expansion of the wood, and q is offset stress in the wood transverse grain plane and mainly causes shear deformation of the wood; defining a P-Q Cartesian coordinate system, drawing a yield surface equation f (P, Q) in the P-Q Cartesian coordinate system, wherein an equivalent stress P in a wood transverse striation plane corresponds to a P axis of the P-Q Cartesian coordinate system, an offset stress Q in the wood transverse striation plane corresponds to a Q axis of the P-Q Cartesian coordinate system, and the yield surface equation f (P, Q) in the P-Q Cartesian coordinate systemThe shape in the system is an ellipse; α is the ratio of the minor axis to the major axis length of the ellipse; p is a radical of0Is the center point of the ellipse; b is the length of the major axis of the ellipse; sigma22And σ33Respectively positive stress, sigma, in the direction of two principal axes in the plane of the transverse grain of the wood23Is the shear stress in the wood cross grain plane; p is a radical ofcCompressive strength, p, for bi-directional compression in the plane of the transverse grain of the woodtTensile strength, p, for bi-directional tension in the plane of the grain of the woodcAnd ptThe coordinate values respectively corresponding to two intersection points of the yield surface equation f (P, Q) and the P axis of the P-Q Cartesian coordinate system respectively have the following calculation formulas:
Figure BDA0003228264340000031
pt＝kt/kYC
Figure BDA0003228264340000032
Figure BDA0003228264340000033
wherein,
Figure BDA0003228264340000034
the stress is the corresponding wood compressive stress after the wood is unidirectionally pressed in the plane of the wood cross grain and the wood is yielded; k and ktAre two coefficients related to wood material; y isTIs the tensile strength in uniaxial tension in the plane of the transverse grain of the wood, YCThe yield strength is the yield strength when the wood is compressed in a single direction in the transverse grain plane; compression strength p of wood pressed in two directions in transverse grain planecIs a variable with an initial value of
Figure BDA0003228264340000035
Its evolution is determined by the hardening equation in the plane of the wood grain.
In some embodiments, the plastic flow equation in the wood grain plane is constructed as:
Figure BDA0003228264340000036
Figure BDA0003228264340000037
Figure BDA0003228264340000038
I2＝σ22+σ33
Figure BDA0003228264340000039
wherein,
Figure BDA00032282643400000310
the plastic strain increment in the wood transverse grain plane is obtained; g is a plastic potential energy function equation;
Figure BDA00032282643400000311
the deviation beta of the plastic potential energy function to the stress sigma is a material coefficient, and the value is more than 1; delta lambda⊥Is a plastic multiplier increment; lambda [ alpha ]⊥Is a delta function; f. of*Substituting the trial stress calculated according to Hooke's law into the calculated value of the yield surface equation f (p, q); i is2And I3A first stress constant and a second stress constant, respectively;
Figure BDA00032282643400000312
and
Figure BDA00032282643400000313
yield surface equation f (p, q) versus second stress constant I, respectively2And a third stress constant I3Calculating a deviation derivative;
Figure BDA00032282643400000314
and
Figure BDA00032282643400000315
respectively a second stress constant I2And a third stress constant I3For lambda⊥Calculating a deviation derivative; n represents the calculation Δ λ⊥Then, the partial derivatives take the value at the time of the nth iteration step.
In some embodiments, the hardening equation in the wood grain plane is constructed as:
Figure BDA0003228264340000041
wherein,
Figure BDA0003228264340000042
is the corresponding wood compressive strain after the wood is unidirectionally pressed in the plane of the wood transverse striation and the wood is yielded.
In some embodiments, the compressive stress of the wood after the wood is unidirectionally stressed in the plane of the wood cross grain and the wood yields
Figure BDA0003228264340000043
The wood compressive strain corresponding to the wood which is unidirectionally pressed in the horizontal grain plane of the wood and after the wood is yielded
Figure BDA0003228264340000044
The relationship (c) is obtained by a one-way compression test.
In some embodiments, the constructed stress-strain relationship in the grain-wise plane of the wood is:
Figure BDA0003228264340000045
wherein σ11Is the positive stress of the wood along the grain direction; sigma12And σ13Respectively, the shearing in two main axis directions in the plane of the grainForce; x is the tensile or compressive strength of the wood along the grain; s is the down grain shear strength of the wood.
The wood striation pressure-bearing constitutive relation model construction device based on the wood weak phase structure provided by the embodiment of the second aspect of the disclosure comprises:
the separation module is used for separating the stress and the strain of the wood along the grain direction and the transverse grain direction;
the first building module is used for building the stress-strain relation of the wood in the elastic stage according to Hooke's law of transverse isotropic materials;
the second construction module is used for separating the equivalent stress causing the volume deformation of the wood from the offset stress causing the shear deformation of the wood in the wood cross grain plane according to the stress characteristic of the pressure bearing of the wood cross grain, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
the third construction module is used for constructing a yield surface equation of the elastoplasticity stage in the wood transverse grain plane according to the non-associated flow rule;
the fourth construction module is used for constructing a hardening equation in the wood cross grain plane according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression and the yield stress during the bidirectional compression; and
and the fifth construction module is used for constructing the stress-strain relation of the wood along the grain direction by adopting a linear elastic model.
A computer-readable storage medium is provided in an embodiment of the third aspect of the present disclosure, and stores computer instructions for causing the computer to execute the above method for building a wood cross grain bearing constitutive relation model.
Drawings
Fig. 1 is an overall flowchart of a method for constructing a wood grain bearing constitutive relation model according to an embodiment of the first aspect of the disclosure.
Fig. 2 is a schematic view of wood and wood material directions set in a construction method provided in an embodiment of the first aspect of the disclosure.
Fig. 3 is a stress-strain curve under the cross grain compressive load and a stress-strain curve calculated by using the wood cross grain pressure-bearing constitutive relation model of the disclosure.
Fig. 4 is a schematic structural diagram of a wood cross grain pressure-bearing constitutive relation model building device provided in an embodiment of a second aspect of the disclosure.
Fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the third aspect of the present disclosure.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
On the contrary, this application is intended to cover any alternatives, modifications, equivalents, and alternatives that may be included within the spirit and scope of the application as defined by the appended claims. Furthermore, in the following detailed description of the present application, certain specific details are set forth in order to provide a better understanding of the present application. It will be apparent to one skilled in the art that the present application may be practiced without these specific details.
Referring to fig. 1, a method for constructing a wood grain bearing constitutive relation model based on a wood weak phase structure provided in an embodiment of the disclosure includes:
separating the stress and strain of the wood along the grain direction and the transverse grain direction;
for wood grain direction:
constructing a stress-strain relation of the wood in an elastic stage according to Hooke's law of transversely viewing isotropic materials;
according to the stress characteristic of wood cross grain bearing, separating equivalent stress causing volume deformation of wood from offset stress causing shear deformation of the wood in a wood cross grain plane, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
constructing a plastic flow equation in the wood transverse grain plane according to the non-correlation flow rule;
constructing a hardening equation in the plane of the wood cross grain according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression of the wood and the yield stress during the bidirectional compression of the wood;
for wood grain-wise direction:
constructing a stress-strain relation in a wood grain-following plane by adopting a linear elastic model or a strength criterion independent of a wood transverse grain plane;
and forming a wood cross grain pressure-bearing constitutive relation model by using the stress-strain relation of the constructed wood in the elastic stage, the yield surface equation of the elastic-plastic stage in the wood cross grain plane, the plastic flow equation in the wood cross grain plane and the stress-strain relation in the wood grain plane.
The method for constructing the wood cross grain pressure-bearing constitutive relation model provided by the embodiment of the first aspect of the disclosure has the following advantages:
the method is based on a weak phase structure when the wood cross grain bears pressure, takes the porous characteristic of the wood into consideration, separates out equivalent stress causing volume deformation of the wood in a wood cross grain plane, takes the relation between yield stress and strain of the wood during unidirectional compression as input, obtains the relation between yield stress and plastic strain during bidirectional compression through conversion, and controls the change of a yield equation by tracking the change of the volume strain of the wood, thereby achieving the purpose of simulating the volume compression and large deformation existing when the wood cross grain bears pressure. The yield equation, the flow equation and the hardening equation of the wood cross grain pressure bearing are established, all parameters in the model have definite physical significance, material parameters are easy to obtain from tests, and the large deformation characteristic of the wood under the compression of the cross grains can be simulated. The constitutive relation model can be used in engineering practice by further writing a calculation program.
In some embodiments, the stress-strain relationship of the wood in the elastic phase is specifically constructed according to the following steps:
the stress-strain relationship of wood in the elastic phase is described using hooke's law across isotropic materials. The grain direction of the wood is taken as a main material axis, and two mutually perpendicular main material axes can be established in a cross grain plane perpendicular to the grain direction. Referring to fig. 2, without loss of generality, three main axes of material can adopt three mutually perpendicular directions of the grain direction 1, the radial direction 2 and the chord direction 3 of the wood.
In some embodiments, the yield surface equation f (p, q) for the elasto-plastic phase in the plane of the constructed wood wales is:
Figure BDA0003228264340000061
Figure BDA0003228264340000062
Figure BDA0003228264340000063
Figure BDA0003228264340000064
Figure BDA0003228264340000065
Figure BDA0003228264340000066
wherein p is equivalent stress in the wood transverse grain plane and mainly causes volume compression or expansion of the wood, and q is offset stress in the wood transverse grain plane and mainly causes shear deformation of the wood; defining a P-Q Cartesian coordinate system, and drawing a yield surface equation f (P, Q) in the coordinate system, wherein an equivalent stress P in a wood transverse grain plane corresponds to a P axis of the P-Q Cartesian coordinate system, an offset stress Q in the wood transverse grain plane corresponds to a Q axis of the P-Q Cartesian coordinate system, and the shape of the yield surface equation f (P, Q) in the P-Q Cartesian coordinate system is an ellipse; alpha is a material parameter, geometric meaning, representing the shape of the yield surface equationDefining the ratio of the minor axis to the major axis of the ellipse of the yield surface; p is a radical of0Is the central point of the ellipse of the yielding surface; b is the length of the major axis of the ellipse of the yield surface; sigma22And σ33Respectively positive stress, sigma, in the direction of two principal axes in the plane of the transverse grain of the wood23Is the shear stress in the wood cross grain plane; p is a radical ofcCompressive strength, p, for bi-directional compression in the plane of the transverse grain of the woodtTensile strength, p, for bi-directional tension in the plane of the grain of the woodcAnd ptThe coordinate values respectively corresponding to two intersection points of the yield surface equation f (P, Q) and the P axis of the P-Q Cartesian coordinate system respectively have the following calculation formulas:
Figure BDA0003228264340000067
pt＝kt/kYC
Figure BDA0003228264340000071
Figure BDA0003228264340000072
wherein,
Figure BDA0003228264340000073
the stress is the corresponding wood compressive stress after the wood is unidirectionally pressed in the plane of the wood cross grain and the wood is yielded; k and ktAre two coefficients related to wood material and can be obtained by experiments; y isTIs the tensile strength in uniaxial tension in the plane of the transverse grain of the wood, YCThe yield strength is the yield strength when the wood is compressed in a single direction in the transverse grain plane; compression strength p of wood pressed in two directions in transverse grain planecIs a variable with an initial value of
Figure BDA0003228264340000074
Its evolution is determined by the hardening equation.
In some embodiments, using the non-associative flow rule, the plastic flow equation in the plane of the wood grain is constructed as:
Figure BDA0003228264340000075
Figure BDA0003228264340000076
Figure BDA0003228264340000077
I2＝σ22+σ33
Figure BDA0003228264340000078
wherein,
Figure BDA0003228264340000079
the plastic strain increment in the wood transverse grain plane is obtained; g is a plastic potential energy function equation;
Figure BDA00032282643400000710
the partial derivative of the plastic potential energy function to the stress sigma is solved, specifically, the partial derivative of G to sigma is expanded into sigma22、σ33And σ23For each component form; beta is a material coefficient, and the value is more than 1; delta lambda⊥Is a plastic multiplier increment; lambda [ alpha ]⊥Is an incremental function; f. of*The trial stress calculated according to Hooke's law is substituted into the yield surface equation f (p, q) to obtain a calculated value; i is2And I3A first stress constant and a second stress constant, respectively;
Figure BDA00032282643400000711
and
Figure BDA00032282643400000712
are respectivelyYield surface equation to second stress constant I2And a third stress constant I3Calculating a deviation derivative;
Figure BDA00032282643400000713
and
Figure BDA00032282643400000714
respectively a second stress constant I2And a third stress constant I3For lambda⊥Calculating a deviation derivative; the subscript n denotes the calculation Δ λ⊥Then, the partial derivatives take the value at the time of the nth iteration step.
In some embodiments, the hardening equation in the plane of the constructed wood grain is:
Figure BDA00032282643400000715
wherein,
Figure BDA00032282643400000716
is the wood compressive stress which is stressed in a single direction in the plane of the wood transverse striation and corresponds to the yield of the wood,
Figure BDA00032282643400000717
is about the corresponding wood compression strain after the wood is unidirectionally pressed in the horizontal grain plane of the wood and the wood is yielded
Figure BDA00032282643400000718
A function of (a);
Figure BDA00032282643400000719
and
Figure BDA00032282643400000720
the relationship (c) is obtained by a one-way compression test.
In some embodiments, the stress-strain relationship in the grain-following plane of the wood may be based on a linear elastic model, or on a strength criterion independent of the grain-crossing plane of the wood, such as the grain-following direction using the following strength criterion:
Figure BDA0003228264340000081
wherein σ11Is the positive stress of the wood along the grain direction; sigma12And σ13Respectively the shear stress of the wood along two main shaft directions in the grain plane; x is the tensile or compressive strength of the wood along the grain; s is the down grain shear strength of the wood.
And when the strength criterion in the grain-following direction is met, adopting an ideal elastic-plastic model.
In order to verify the effectiveness of the method for constructing the wood cross grain pressure-bearing constitutive relation model provided by the embodiment of the first aspect of the disclosure, the wood cross grain pressure-bearing constitutive relation model constructed by the method disclosed by the disclosure is used for simulating the pressure-bearing performance of the wood cross grain and is compared with the measured value of a test, the result is shown in fig. 3, and it can be known from fig. 3 that the wood cross grain pressure-bearing constitutive relation model constructed by the method disclosed by the disclosure has better simulation accuracy.
The wood cross grain pressure-bearing constitutive relation model construction device based on the wood weak phase structure provided by the embodiment of the second aspect of the disclosure has the structure shown in fig. 4, and includes:
the separation module is used for separating the stress and the strain of the wood along the grain direction and the transverse grain direction;
the first building module is used for building the stress-strain relation of the wood in the elastic stage according to Hooke's law of transverse isotropic materials;
the second construction module is used for separating the equivalent stress causing the volume deformation of the wood from the offset stress causing the shear deformation of the wood in the wood cross grain plane according to the stress characteristic of the pressure bearing of the wood cross grain, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
the third construction module is used for constructing a yield surface equation of the elastoplasticity stage in the wood transverse grain plane according to the non-associated flow rule;
the fourth construction module is used for constructing a hardening equation in the wood cross grain plane according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression and the yield stress during the bidirectional compression; and
and the fifth construction module is used for constructing the stress-strain relation of the wood along the grain direction by adopting a linear elastic model.
In order to implement the foregoing embodiment, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor, and is used to execute the method for constructing the wood grain-transverse-grain-bearing constitutive relation model of the foregoing embodiment.
Referring now to FIG. 5, a block diagram of an electronic device 900 suitable for use in implementing embodiments of the present disclosure is shown. It should be noted that the electronic device 900 may include, but is not limited to, a mobile terminal such as a mobile phone, a notebook computer, a digital broadcast receiver, a PDA (personal digital assistant), a PAD (tablet computer), a PMP (portable multimedia player), a car terminal (e.g., car navigation terminal), etc., and a fixed terminal such as a digital TV, a desktop computer, a server, etc. The electronic device shown in fig. 5 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present disclosure.
As shown in fig. 5, the electronic device 900 may include a processing means (e.g., a central processing unit, a graphics processor, etc.) 901 that may perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM)902 or a program loaded from a storage means 908 into a Random Access Memory (RAM) 903. In the RAM 903, various programs and data necessary for the operation of the electronic apparatus 900 are also stored. The processing apparatus 901, the ROM 902, and the RAM 903 are connected to each other through a bus 904. An input/output (I/O) interface 905 is also connected to bus 904.
Generally, the following devices may be connected to the I/O interface 905: an input device 906 including, for example, a touch screen, a touch pad, a keyboard, a mouse, a camera, a microphone, and the like; an output device 907 including, for example, a Liquid Crystal Display (LCD), a speaker, a vibrator, and the like; storage 908 including, for example, magnetic tape, hard disk, etc.; and a communication device 909. The communication device 909 may allow the electronic apparatus 900 to perform wireless or wired communication with other apparatuses to exchange data. While fig. 5 illustrates an electronic device 900 having various means, it is to be understood that not all illustrated means are required to be implemented or provided. More or fewer devices may alternatively be implemented or provided.
In particular, according to an embodiment of the present disclosure, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, the present embodiments include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method illustrated in the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication device 909, or installed from the storage device 908, or installed from the ROM 902. The computer program performs the above-described functions defined in the methods of the embodiments of the present disclosure when executed by the processing apparatus 901.
It should be noted that the computer readable medium in the present disclosure can be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In contrast, in the present disclosure, a computer readable signal medium may comprise a propagated data signal with computer readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, optical cables, RF (radio frequency), etc., or any suitable combination of the foregoing.
The computer readable medium may be embodied in the electronic device; or may exist separately without being assembled into the electronic device.
The computer readable medium carries one or more programs which, when executed by the electronic device, cause the electronic device to: separating the stress and strain of the wood along the grain direction and the transverse grain direction; constructing a stress-strain relation of the wood in an elastic stage according to Hooke's law of transversely viewing isotropic materials; according to the stress characteristic of wood cross grain bearing, separating equivalent stress causing volume deformation of wood from offset stress causing shear deformation of the wood in a wood cross grain plane, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress; constructing a plastic flow equation in the wood transverse grain plane according to the non-correlation flow rule; constructing a hardening equation in the plane of the wood cross grain according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression of the wood and the yield stress during the bidirectional compression of the wood; and (3) constructing the stress-strain relation of the wood along the grain direction by adopting a linear elastic model.
Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + +, python, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by a program instructing associated hardware to complete, and the developed program may be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (8)

1. A wood cross grain pressure-bearing constitutive relation model construction method based on a wood weak phase structure is characterized by comprising the following steps:
separating the stress and strain of the wood along the grain direction and the transverse grain direction;
constructing a stress-strain relation of the wood in an elastic stage according to Hooke's law of transversely viewing isotropic materials;
according to the stress characteristic of wood cross grain bearing, separating equivalent stress causing volume deformation of wood from offset stress causing shear deformation of the wood in a wood cross grain plane, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
constructing a plastic flow equation in the wood transverse grain plane according to the non-correlation flow rule;
constructing a hardening equation in the plane of the wood cross grain according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression of the wood and the yield stress during the bidirectional compression of the wood;
and (3) constructing a stress-strain relation in the wood grain-following plane by adopting a linear elastic model or a strength criterion independent of the wood grain-crossing plane.
2. The method for constructing the wood cross grain pressure-bearing constitutive relation model according to claim 1, wherein the yield surface equation of the elastoplasticity stage in the wood cross grain plane is constructed as f (p, q), and the expression is as follows:
Figure FDA0003228264330000011
Figure FDA0003228264330000012
Figure FDA0003228264330000013
Figure FDA0003228264330000014
Figure FDA0003228264330000015
wherein p is equivalent stress in the wood transverse striation plane and mainly causes volume pressure of the woodShrinking or expanding, wherein q is the offset stress in the horizontal grain plane of the wood and mainly causes the shear deformation of the wood; defining a P-Q Cartesian coordinate system, and drawing a yield surface equation f (P, Q) in the P-Q Cartesian coordinate system, wherein an equivalent stress P in a wood transverse striation plane corresponds to a P axis of the P-Q Cartesian coordinate system, an offset stress Q in the wood transverse striation plane corresponds to a Q axis of the P-Q Cartesian coordinate system, and the shape of the yield surface equation f (P, Q) in the P-Q Cartesian coordinate system is an ellipse; α is the ratio of the minor axis to the major axis length of the ellipse; p is a radical of0Is the center point of the ellipse; b is the length of the major axis of the ellipse; sigma22And σ33Respectively positive stress, sigma, in the direction of two principal axes in the plane of the transverse grain of the wood23Is the shear stress in the wood cross grain plane; p is a radical ofcCompressive strength, p, for bi-directional compression in the plane of the transverse grain of the woodtTensile strength, p, for bi-directional tension in the plane of the grain of the woodcAnd ptThe coordinate values respectively corresponding to two intersection points of the yield surface equation f (P, Q) and the P axis of the P-Q Cartesian coordinate system respectively have the following calculation formulas:
Figure FDA0003228264330000016
pt＝kt/kYC
Figure FDA0003228264330000021
Figure FDA0003228264330000022
wherein,
Figure FDA0003228264330000023
the stress is the corresponding wood compressive stress after the wood is unidirectionally pressed in the plane of the wood cross grain and the wood is yielded; k and ktAre two coefficients related to wood material; y isTIs arranged in the horizontal grain plane of the woodTensile Strength in tensile, YCThe yield strength is the yield strength when the wood is compressed in a single direction in the transverse grain plane; compression strength p of wood pressed in two directions in transverse grain planecIs a variable with an initial value of
Figure FDA0003228264330000024
Its evolution is determined by the hardening equation in the plane of the wood grain.
3. The method for constructing the wood cross grain pressure-bearing constitutive relation model according to claim 2, wherein the constructed plastic flow equation in the wood cross grain plane is as follows:
Figure FDA0003228264330000025
Figure FDA0003228264330000026
Figure FDA0003228264330000027
I2＝σ22+σ33
Figure FDA0003228264330000028
wherein,
Figure FDA0003228264330000029
the plastic strain increment in the wood transverse grain plane is obtained; g is a plastic potential energy function equation;
Figure FDA00032282643300000210
the deviation of the stress sigma is calculated by a plastic potential energy function; beta is a material coefficient, and the value is more than 1;Δλ⊥is a plastic multiplier increment; lambda [ alpha ]⊥Is a delta function; f. of*Substituting the trial stress calculated according to Hooke's law into the calculated value of the yield surface equation f (p, q); i is2And I3A first stress constant and a second stress constant, respectively;
Figure FDA00032282643300000211
and
Figure FDA00032282643300000212
yield surface equation f (p, q) versus second stress constant I, respectively2And a third stress constant I3Calculating a deviation derivative;
Figure FDA00032282643300000213
and
Figure FDA00032282643300000214
respectively a second stress constant I2And a third stress constant I3For lambda⊥Calculating a deviation derivative; n represents the calculation Δ λ⊥Then, the partial derivatives take the value at the time of the nth iteration step.
4. The method for constructing the wood cross grain pressure-bearing constitutive relation model according to claim 3, wherein the hardening equation in the wood cross grain plane is constructed by:
Figure FDA00032282643300000215
wherein,
Figure FDA00032282643300000216
is the corresponding wood compressive strain after the wood is unidirectionally pressed in the plane of the wood transverse striation and the wood is yielded.
5. The method for constructing a wood cross grain bearing constitutive relation model according to claim 4The method is characterized in that the wood compressive stress is unidirectionally stressed in the plane of the transverse grains of the wood and corresponds to the wood compressive stress after the wood is yielded
Figure FDA00032282643300000217
The wood compressive strain corresponding to the wood which is unidirectionally pressed in the horizontal grain plane of the wood and after the wood is yielded
Figure FDA0003228264330000031
The relationship (c) is obtained by a one-way compression test.
6. The method for constructing the wood cross grain pressure-bearing constitutive relation model according to claim 1, wherein the constructed stress-strain relation in the wood cross grain plane is as follows:
Figure FDA0003228264330000032
wherein σ11Is the positive stress of the wood along the grain direction; sigma12And σ13Respectively the shear stress of the wood along two main shaft directions in the grain plane; x is the tensile or compressive strength of the wood along the grain; s is the down grain shear strength of the wood.
7. The utility model provides a timber striation pressure-bearing constitutive relation model construction device based on timber weak phase structure which characterized in that includes:
the separation module is used for separating the stress and the strain of the wood along the grain direction and the transverse grain direction;
the first building module is used for building the stress-strain relation of the wood in the elastic stage according to Hooke's law of transverse isotropic materials;
the second construction module is used for separating the equivalent stress causing the volume deformation of the wood from the offset stress causing the shear deformation of the wood in the wood cross grain plane according to the stress characteristic of the pressure bearing of the wood cross grain, and constructing a yield surface equation of an elastoplasticity stage in the wood cross grain plane based on the equivalent stress and the offset stress;
the third construction module is used for constructing a yield surface equation of the elastoplasticity stage in the wood transverse grain plane according to the non-associated flow rule;
the fourth construction module is used for constructing a hardening equation in the wood cross grain plane according to the evolution relation of the yield stress along with the strain during the unidirectional compression of the wood and the relation between the yield stress during the unidirectional compression and the yield stress during the bidirectional compression; and
and the fifth construction module is used for constructing the stress-strain relation of the wood along the grain direction by adopting a linear elastic model.
8. A computer-readable storage medium storing computer instructions for causing a computer to execute the method of constructing a wood grain bearing constitutive relation model according to any one of claims 1 to 6.
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